Okay, from the long range shooting aspect of it, the theory is that if you let the copper build up a little, essentially being burnished into the rifling, that this will fill in microscopic imperfections leading to a more uniformly smooth barrel. Some barrels are lapped to fix these imperfections, some don't worry about it. The better the barrel, the less the problem. I have a cut rifle Satern barrel on one AR and it fires sub-MOA groups with a clean barrel or a dirty one --but I don't let it get all that diry.
When I clean, I run wet patches of plain Hoppes #9. They make a copper fouling formula, but I don't use it, and you'll understand why later. It has ammonia in it I think, and you want to try and get all that out no matter what you use if it has ammonia in it. Since I use Hoppes to clean the bolt and other parts, I just use the plain stuff. For the barrel, I pretty much only use the plain #9, and I use patches and sometimes a bore mop. I let it soak in a minute before running the brushes, then I go back behind with patches --they usually come out dark the first time. Then I repeat this until I can run the brush and follow it with patches and have the patches come out fairly clean. THEN I run a couple of oiled patches through to clean out the #9, then I run a clean patch through to "dry" up all the excess. This gives me a good clean barrel, and I know what to expect each time.
But after one or two thousand rounds, I'll clean it up this way, but then I'll go through and use Sweets afterwards. You want the barrel clean and dry before putting the Sweets in it. I'll let it soak in for 15-30 minutes, then I'll run some patches through, some with more Sweets on it, and keep cleaning until I stop getting blue stains on the patches. If I keep getting blue stains with the patches with Sweets on them, then I'll go ahead and soak some more and run those through again and let it soak more and repeat until the patches come out with no stains. At this point, you'll have all the copper out but you aren't done yet.
Once you dissolve the copper, you'll expose more carbon, but the Sweets won't dissolve that. So you have to clean the barrel over again from step one using the plain #9. You need to do this for two reasons, one is to clean out the Sweets because you don't want to leave any of that behind, and two is because once you remove the copper, you will uncover more fouling. You may be surprised when you go to clean it that the patches start coming out black again after running the brush. But this only illustrates the burnishing effect the bullets going down the barrel have on the copper and carbon fouling in the barrel. When thin layers of copper and carbon are burnished in a barrel, layer on top of layer, it is possible to clean it with CLP and have it LOOK clean when it isn't. But these layers build up and change in thickness and uniformity with each shot, thus affecting consistency. Accuracy is dependent upon consistency.
If during the cleaning process you take note of your groups with clean vs. dirty and find that the diry barrel after so many shots gives you better groups, I would suggest getting a small jar of JB Bore Paste. That stuff does wonders for cleaning and polishing a barrel. It doesn't do anything that will affect a warranty either. It is also good to use after the Sweets to get all that tough, old, dry and burnished carbon out. You can get a barrel spotless with it with time and patience. And if you have microscopic flaws in the barrel, this stuff is just abrasive enough to fix that. Good, good stuff; a little goes a long way and a tiny jar lasts forever.
Some folks think their clean barrel shoots worse than their dirty barrel because some don't actually have a clean barrel. They cleaned it, but they didn't remove the burnished in stuff. By cleaning, they may have made the barrel surface uneven by cleaning out softer areas but not harder ones. Remember, burnished in carbon and copper look like shiny steel when you shine a flashlight down the bore. Firing a few more rounds will fill those places back in first, and then they get their accuracy back. I'd argue a thorough cleaning would be superior. Others did clean it well, but they uncovered the imperfections in the barrel again. Now they have to fire more rounds, which will build up around or in the imperfections first, thus "fixing" it.
By the way, I've seen 'em so dirty that I could get 'em wet, put 'em away overnight to soak, clean and repeat --over and over and over again-- and not get it clean. Magnificently dirty, but it had been cleaned with CLP only for years. This particular one was a SAW with two barrels. I finally got clean barrels, but it took a long time, and I was surprised to find that my rifling wasn't worn, no, it was fine, it was that the grooves were filled in with copper and carbon!
There ain't no magic fix and guy on here is right, nobody can tell you the right thing to do regarding this, but what I say is the truth, and if you clean your barrels well and do it right (there are a few right ways, this is one of them and what I use for rifles) then you'll at least get a consistent barrel to work with, a predictable one, and that is VERY important in my book. If you have to tune it with fouling, something is wrong, find a better barrel maker or use your warranty on that one.
I hope this helps, Happy New Year!